Income Per Share - Schedule of Computation of Diluted Income Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 01, 2025	Feb. 24, 2024	Mar. 01, 2025	Feb. 24, 2024
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 24,459	$ 20,457	$ 67,564	$ 62,782
As reported - Basic (in shares)	18,567	18,696	18,577	18,700
As reported - Diluted	$ 24,459	$ 20,457	$ 67,564	$ 62,782
As reported - Diluted (in shares)	18,649	18,754	18,653	18,758
As reported - Diluted (in dollars per share)	$ 1.31	$ 1.09	$ 3.62	$ 3.35
Common Stock
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 20,559	$ 17,188	$ 56,778	$ 52,754
As reported - Basic (in shares)	15,009	15,106	15,011	15,110
As reported - Basic (in dollars per share)	$ 1.37	$ 1.14	$ 3.78	$ 3.49
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	82	58	76	58
As reported - Diluted (in dollars per share)	$ 1.31	$ 1.09	$ 3.62	$ 3.35
Class B Common Stock
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 3,900	$ 3,269	$ 10,786	$ 10,028
As reported - Basic (in shares)	3,558	3,590	3,566	3,590
As reported - Basic (in dollars per share)	$ 1.1	$ 0.91	$ 3.02	$ 2.79